{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Approximated Off-axis Parabola via Chebyshev Surface"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from optiland import optic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize an optic system\n",
    "system = optic.Optic()\n",
    "\n",
    "# add surfaces to the system\n",
    "system.add_surface(index=0, thickness=np.inf)  # object at infinity\n",
    "\n",
    "coefficients = np.array(\n",
    "    [\n",
    "        [\n",
    "            1.24694339e-05,\n",
    "            4.67020030e-03,\n",
    "            3.62355202e-03,\n",
    "        ],  # optimized chebyshev coefficients\n",
    "        [5.46006887e-11, -1.03813427e-07, -8.01598028e-08],\n",
    "        [-5.81261746e-03, -5.21668069e-03, 4.53883501e-03],\n",
    "    ],\n",
    ")\n",
    "\n",
    "# add mirror surface\n",
    "system.add_surface(\n",
    "    index=1,\n",
    "    thickness=-85.64,\n",
    "    radius=-185,\n",
    "    conic=0,\n",
    "    material=\"mirror\",\n",
    "    is_stop=True,\n",
    "    dy=36,\n",
    "    surface_type=\"chebyshev\",\n",
    "    norm_x=100,\n",
    "    norm_y=100,\n",
    "    coefficients=coefficients,\n",
    ")\n",
    "\n",
    "system.add_surface(index=2)  # image plane\n",
    "\n",
    "# add aperture\n",
    "system.set_aperture(aperture_type=\"EPD\", value=33)\n",
    "\n",
    "# add field\n",
    "system.set_field_type(field_type=\"angle\")\n",
    "system.add_field(y=0)\n",
    "\n",
    "# add wavelength\n",
    "system.add_wavelength(value=0.587, is_primary=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "system.draw(num_rays=10)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
